Car noticeably pulls to the left when pressing accelerator at speeds 30 mph and up.
If I leave steering wheel alone it slightly ( 4-5 degrees) turns to the right on its own during acceleration keeping car more or less straight.

Some background:
front right tire lost pressure on hwy but the car was still driven for 1-2 miles (I wasn't there). Finally stopped, changed tire to spare and continued driving. The tire was severely damaged with huge holes in side walls. 2 days later both front tires were replaced with "BFGoodrich g-Force Sport comp-2" 225/50ZR17. Shop did the alignment as well although nobody asked them to. I haven't got a chance to drive it between incident and tire replacement so I can't tell if the change in steering behavior was result of incident or new tires. I jacked up the car later and checked play in ball joints or steering components and found none, everything feels tight.

hope someone can shed light on this as I'm fairly puzzled at the moment:
- alignment problem?
- tire problem?
- something got bent?

 

Check tie rod ends?? I doubt you bent your rim though possible but what you describe doesn't sound like it.

 

Actually if tie rods are bad they wouldn't/shouldn't give you an alignment. Is this a reputable shop??

 

It turns out it was LCA bushing, at least passenger side but I'll replace both anyway. Talk about coincidence: I replaced both LCAs 2 years ago and now LCA front end visibly moves in the bushing when I'm moving wheel left-to-right holding my arms at 9 and 3 o'clock. When I was checking myself I was expecting some kind of 'solid' play (ball joint / ends) and since I wasn't watching all suspension parts I missed the play in the bushing. Now I had a helper and he noticed play right away. I had a feeling shop noticed something too and did alignment knowing very well I'd come back again very soon. Why this problem became much more noticeable after replacing tires remains a mystery. I recall now some faint noises from the front suspension before but I was putting off doing anything knowing the components there are fairly fresh. Boy was I wrong.

 

Are the bfg's directional tires? I put my Federals on the wrong direction on accident and it caused a major pull issue. Once I put them on in the correct direction the problem was gone.

 

They're and I checked that the very first thing- they were installed correctly. Anyway, the culprit was found, parts already arrived so I'll do the replacement this weekend.