he showed signs of caring throughout the series

He does, but hardly in a romantic sense. It's more of a father-daughter/teacher-student kind of relationship.

Yes, of course. But the nature of it... Depends... of the canon?

Manga wise. He seemed to respect her bravery in the beginning, but if he REALLY cared for her, he wouldn't have killed her and turned her into a vampire. Because, at this point of canon, he was conflicted with the vampire nature (he got over it only in VOLUME NINE) and wouldn't have wished this to his ENEMY, Anderson. So huh... He doesn't even look pleased when he carries her and introduces her to Integra (defensively telling his master he had no other choice at her hot accusations). It's not that he called her Police Girl for kicks, but because Kouta Hirano didn't really care about Seras' character's background or name or personality until later on (he admitted it). He lined down his protagonists, Alucard and Integra, and she was the support cast "Police Girl". So this has more a meta reason ;P I think he has a parental care for her, as of a mentor to a heir/successor. But this develops eventually... Let's also remember that /Alucard killed her first/ and if she didn't want to become a vampire later, she would have bleed to death and he would have brushed it off. It's not the natural affection he has for Integra (who he saves on spot, instead of killing her and let her choose). He eventually cares for her as a heir to him, first admiration but... nothing big she was disposable enough to shoot to death. Then saw her usefulness (he remarks that if she wouldn't perform so good in her duty it wouldn't make sense to have turned her into a vampire in v1) and begrudgingly developed a certain familiar fondness. He trusts her to be strong, like a good teacher.

OVA wise... there are instances that are softer than the manga. Alucard looks happy when she awakes (as opposed to apathetic/annoyed look: link), holds her hand when she calls for her mother and father. So basically, it's the same as the manga, only with more clear fondness early on. OVA team pegs her as his "cute daughter figure", so.

TV series wise, his relationship is less platonic, and yes, he cared for her in a more romantic way because... (according to Gonzo), when they met her eyes reminded him to Integra's when they met? Still has some fatherly/teacher overtones, but less platonic because Alucard unsuccessfully tries to 'replace' Integra but can't. He even throws her at Integra's face as the first thing he does (unlike the manga, where he defends himself, here even taunts Integra in his subtle way). OF course, he does care for Seras as her own person eventually too, but it's clear that she wouldn't be a good Integra to his childish disappointment.

yes this is really true

It's very obvious yes

If he wouldn't care for her, he wouldn't conciser being her master and would never save her. They have not bad moments though...

yeah :DD but i love them together. :D

1. He shot her through the heart to kill the FREAK that was embracing her (holding her hostige) and turned he rin to a vampire when she was dying even though he could of do a head-shot and she wouldn't had to die, she would be living her normal life by now but she still did it another way and to say he gave her much more that she has when she was a human. [Hellsing: Episode 1]
2. When fighting with Andersin and doing him a headshot when Alucard thought hes dead, he walked to seras and offered her a hand. [Hellsing: Episode 2].
3. He saved her a couple of times...
4. When a fight with Incognito, Seras came to help Aucard (bouth him bullets) he yelled her to run ("Run away, now!!"). [Hellsing: Episode 13].
And may more...
It's very obvious he cares for his fledging.

Although he doesn't call Seras by her regular name, she was ready to make the sacrifice. And when they meet again in the OVA after the events of OVA 7, Alucard will certainly drop jaw.

Isn't it obvious already? He shown much signs of caring for here.

Te reason he was smiling when she was nearly dead is beacus he always smiles. And before that, he shouted at her to run and had a very serious expression. Which means he really cares fore her.
And just because he doesn't call her by her real name, does not mean he doesn't care for her. He's her master and she's his fledgling. It's a cute nick name if you ask me. And about turning her into a vampire, it was the first time they've met! Of course he didn't care for her at first! But they spend time together and got attached? Something like that... So yeah, he cars for her. ;P

Yes, of course. But the nature of it... Depends... of the canon?

Manga wise. He seemed to respect her bravery in the beginning, but if he REALLY cared for her, he wouldn't have killed her and turned her into a vampire. Because, at this point of canon, he was conflicted with the vampire nature (he got over it only in VOLUME NINE) and wouldn't have wished this to his ENEMY, Anderson. So huh... He doesn't even look pleased when he carries her and introduces her to Integra (defensively telling his master he had no other choice at her hot accusations). It's not that he called her Police Girl for kicks, but because Kouta Hirano didn't really care about Seras' character's background or name or personality until later on (he admitted it). He lined down his protagonists, Alucard and Integra, and she was the support cast "Police Girl". So this has more a meta reason ;P I think he has a parental care for her, as of a mentor to a heir/successor. But this develops eventually... Let's also remember that /Alucard killed her first/ and if she didn't want to become a vampire later, she would have bleed to death and he would have brushed it off. It's not the natural affection he has for Integra (who he saves on spot, instead of killing her and let her choose). He eventually cares for her as a heir to him, first admiration but... nothing big she was disposable enough to shoot to death. Then saw her usefulness (he remarks that if she wouldn't perform so good in her duty it wouldn't make sense to have turned her into a vampire in v1) and begrudgingly developed a certain familiar fondness. He trusts her to be strong, like a good teacher.

OVA wise... there are instances that are softer than the manga. Alucard looks happy when she awakes (as opposed to apathetic/annoyed look: link), holds her hand when she calls for her mother and father. So basically, it's the same as the manga, only with more clear fondness early on. OVA team pegs her as his "cute daughter figure", so.

TV series wise, his relationship is less platonic, and yes, he cared for her in a more romantic way because... (according to Gonzo), when they met her eyes reminded him to Integra's when they met? Still has some fatherly/teacher overtones, but less platonic because Alucard unsuccessfully tries to 'replace' Integra but can't. He even throws her at Integra's face as the first thing he does (unlike the manga, where he defends himself, here even taunts Integra in his subtle way). OF course, he does care for Seras as her own person eventually too, but it's clear that she wouldn't be a good Integra to his childish disappointment.

I said yes, but the way he cares is rather possesive IMO. She's part of him, akin to him. Alucard is a really old vampire and wasn't exactly filled with warm, fuzzy sentiments as a mortal, so his version of caring isn't quite up to human standards.