“pensando en ti” vs. “pensando de ti” vs. “pensándote”

Question

When using the verb pensar to describe thinking about a person, there are at least three options:

• Estoy pensando en ti.
• Estoy pensando de ti.
• Estoy pensándote.

What are the differences between these three forms? What does each form imply? What about in sentences about objects, not people:

• Estoy pensando en eso.
• Estoy pensando de eso.
• Estoy pensándolo.

Answer 1

When trying to express you are thinking of someone, you always use pensar en. Without en preposition, you could express something strange, as of you are trying to "invent" or "deducing" someone:

• Estoy pensando en ti  →  I'm thinking of you.
• Estoy pensándote  →  (something like: trying to deduce you, but very very strange).

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On the other hand, when talking about objects, if you omit the en preposition, you express the idea of "think about, think through", that is to say, when you put all your mind trying to devise the pros and cons of something (in Spanish could be similar to considerar):

• Estoy pensándolo  →  I'm thinking it through.

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When using pensar de (as says @jrdioko in a comment to this answer), you express what you think about someone or something, that is to say, your opinion about him/her/it:

• No quiero que piense de mí que soy una desagradecida  →  I don't want him to think I'm ungrateful.