I've just started to get into Texture Painting, and I've started one for a model I've made. Now I need to add black lines onto the mesh in places that make the model resemble a 3D outlined character. However, as I started painting the black lines, they came out pixelated as I stroke them. Is this an issue of the map dimensions? Where I would have to greatly increase the size of it in order to have clean lines up close? Please help.
I would suggest giving the area where you need detail more real estate on the UV map. If that isn't enough, increase the size of the image. You can always bake down to a smaller image and a different UV map later.
I know this answer is actually not painting per se, but have you thought about using a second uv mapping and setting it to the standard all faces mapped to the one image - and then you can use a single square image with a colored border and then bake the texture to the previous uv mapped blank texture. Every face will get this outline then, but then it will be transferred to your painting image.